A cat meows incessantly when alone because it lacks a sense of security. This could be due to unfair treatment by its previous owner, or separation from its mother shortly after birth. These are times when cats are most vulnerable and insecure. 
How to address a cat's lack of security:
At this time, it is recommended that the owner provide more emotional companionship to the cat. Secondly, if the cat is left alone for a long time and the owner is very busy, some cats will meow in hopes of attracting the owner's attention and getting their company.
